We propose to have grown and to characterize a promising class of fast, bright, heavy phosphors -- rare earth doped Lu2SiO5 (LuSO) and LuA1O3 (LuAO) -- with the goal of providing the scintillators with which the sensitivity of Positron Emission Tomography (PET) cameras can be increased. From what is known of the only existing single crystal example of the class, Lu2SiO5:Ce3+ (LSO), these materials will be bright and have good photoelectric-to-Compton stopping power for 511 keV photons, fast rise times, good energy resolution, short luminescence lifetimes, and resistance to chemical attack, mechanical abuse, and radiation damage. These properties offer a decisive advantage over the current standard PET scintillators, sodium iodide (NaI:Tl) and bismuth germanate (BGO). Our study has three goals: (1) Estimate by computer calculation the decay and luminescent properties of a wide variety of LuSO and LuAO doped with a range of concentrations of a number of rare earth ions; (2) Obtain samples of those LuSO and LuAO variants with the most promising PET properties; and (3) Evaluate experimentally these candidate materials for PET applications. PROPOSED COMMERCIAL APPLICATION: The physical and luminescence properties of lutetium-based scintillators, when realized in high-quality single crystals, should find broad application ill both medical and industrial radiological detectors.